A General Framework for Computation of Biomedical Image Moments

Abstract

Image moments have been successfully used as images’ content descriptors for several decades. Their ability to fully describe an image by encoding its contents in a compact way makes them suitable in many disciplines of the engineering life, such as image analysis (Sim et al., 2004), image watermarking (Papakostas et al., 2010a) and pattern recognition (Papakostas et al., 2005, 2007, 2009a, 2010b). Apart from the geometric moments, which are firstly introduced, several moment types have been presented due time (Flusser et al., 2009). Orthogonal moments are the most popular moments widely used in many applications owing to their orthogonality property that permits the reconstruction of the image by a finite set of its moments with minimum reconstruction error. This orthogonality property comes from the nature of the polynomials used as kernel functions, which they constitute an orthogonal base. As a result the orthogonal moments have minimum information redundancy meaning that different moment orders describe different image parts of the image. The most well known orthogonal moment families are: Zernike, Pseudo-Zernike, Legendre, Fourier-Mellin, Tchebichef, Krawtchouk, dual Hahn moments, with the last three ones belonging to the discrete type moments since they are defined directly to the image coordinate space, while the first ones are defined in the continue space. Recently, there is an increased interest on applying image moments in biomedical imaging, with the reconstruction of medical images (Dai et al., 2010; Papakostas et al., 2009b; Shu et al., 2007; Wang & Sze, 2001) and the description of image’s parts with particular properties (Bharathi & Ganesan, 2008; Iscan et al., 2010; Li & Meng, 2009; Liyun et al., 2009) by distinguishing diseased areas from the healthy ones, being the most active research directions the scientists work with. Therefore, a method that computes fast and accurate the orthogonal moments of a biomedical image is of great importance. Although many algorithms and strategies (Papakostas et al., 2010c) have been proposed in the past, these methodologies handle the biomedical images as “every-day” images, meaning that they are not making use of specific properties of the image in process. The authors have made a first attempt to compute the Krawtchouk moments of biomedical images by taking advantage of the inherent property of the biomedical image to have limited number of different intensity values (Papakostas et al., 2009c). Based on this observation and by applying the ISR method (Papakostas et al., 2008a) an image is